This paper considers the problem of synthesising a static output feedback (SOF) subject to arbitrary information structure constraints; in particular, the plants can be non-strictly proper. In such a case, the existing methods are hardly applicable except few special cases. A general approach that significantly differs from the existing methods is proposed that is able to deal with the most general case with the feature that both finite-frequency and full-frequency H-infinity performance specifications can be addressed in a unified manner. Sufficient solvability conditions are derived in terms of a set of finite-frequency positive real and strictly positive real conditions of linear matrix inequalities (LMIs) form. Some frequency-dependent matrices are introduced into the design with the merit of making the conditions less restrictive. Several numerical examples are given that demonstrate the efficacy of the proposed approach, including applications to vehicle platooning.